The present invention relates to channel estimation in mobile communication systems, and more particularly to methods and apparatuses that perform channel estimation with lower computational intensity.
Mobile radio telephony is characterized, among other things, by multipath propagation of the radio signal that is transmitted between base stations (BSs) and mobile stations (MSs). Because different rays of the transmitted signal may take different paths before arriving at a receiver""s antenna, some rays are received later than others by the receiver. The resulting received signal, then, includes one or more echoes of the transmitted signal. When the information transmitted in the signal consists of digital symbols, these echoes are referred to as Inter-Symbol Interference (ISI). ISI detrimentally affects a receivers ability to determine the informational content of the received signal.
In order to reduce or eliminate ISI in a received signal, it is known to use equalizers in the receiver. This will be further described with reference to systems that utilize Code Division Multiple Access (CDMA) techniques to distinguish between the signals associated with different users. It will be recognized, however, that CDMA is but one of many possible examples (e.g., Time Division Multiple Access, or xe2x80x9cTDMAxe2x80x9d being another such example) of radio systems that employ a RAKE receiver or equalizers to address the problem of multipath propagation.
The basic idea in a CDMA system is to separate different users, base stations, and services by means of unique spreading sequences/codes. In one type of CDMA system, the informational data stream to be transmitted is impressed upon a much higher rate data stream known as a signature or spreading sequence. Typically, the signature sequence data are binary, thereby providing a bit stream. One way to generate this signature sequence is with a pseudo-noise (PN) process that appears random, but can be replicated by an authorized receiver. The informational data stream and the high bit rate signature sequence stream are combined by multiplying the two bit streams together, assuming the binary values of the two bit streams are represented by +1 or xe2x88x921. This combination of the higher bit rate signal with the lower bit rate data stream is called spreading the informational data stream signal. Each informational data stream or channel is allocated a unique signature sequence.
A plurality of spread information signals modulate a radio frequency carrier, for example by binary phase shift keying (BPSK), and are jointly received as a composite signal at the receiver. Each of the spread signals overlaps all of the other spread signals, as well as noise-related signals, in both frequency and time. If the receiver is authorized, then the composite signal is correlated with one of the unique signature sequences, and the corresponding information signal can be isolated and despread. If quadrature phase shift keying (QPSK) modulation is used, then the signature sequence may consist of complex numbers (having real and imaginary parts), where the real and imaginary parts are used to modulate respective ones of two carriers at the same frequency, but ninety degrees out of phase with respect to one another.
Traditionally, a signature sequence is used to represent one bit of information. Receiving the transmitted sequence or its complement indicates whether the information bit is a +1 or xe2x88x921, sometimes denoted xe2x80x9c0xe2x80x9d or xe2x80x9c1xe2x80x9d. The signature sequence usually comprises N bits, and each bit of the signature sequence is called a xe2x80x9cchipxe2x80x9d. The entire N-chip sequence, or its complement, is referred to as a transmitted symbol. The conventional receiver, such as a RAKE receiver, correlates the received signal with the complex conjugate of the known signature sequence to produce a correlation value. When a large positive correlation results, a xe2x80x9c0xe2x80x9d is detected; when a large negative correlation results, a xe2x80x9c1xe2x80x9d is detected.
It will be understood, then, that the rate of the spreading code (usually referred to as the chip rate) is larger than the information symbol rate. The code rate divided by the information symbol rate is referred to as the spreading factor (Sf). In a system with the transmission of several users being separated by different spreading codes, the code that separates these users is referred to as the long code. By correlating the composite signal with the conjugate of one of the used codes in a receiver, the corresponding user information is recreated while signals related to other users are experienced as noise.
In order to overcome the multipath characteristics in a mobile radio channel, the RAKE receiver and the ray searcher are two essential units for the Wideband Code Division Multiple Access (W-CDMA) technology being standardized under the name IMT2000. (See, e.g., IMT-2000 Study Committee Air-interface WG, SWG2, xe2x80x9cVolume 3 Specifications of Air-interface for 3G Mobile Systemxe2x80x9d, Ver. 0-3.1, December 1997.) An exemplary RAKE receiver is illustrated in FIG. 1. Briefly, the fundamental idea with the RAKE is to synchronize each of the relevant multipath components of the input radio signal to a rather simple receiver. (See, e.g., J. G. Proakis, Digital Communications, McGraw-Hill, 1983). The simple receiver is often referred to as an arrangement of RAKE fingers. Six RAKE fingers 101 are depicted in the exemplary receiver of FIG. 1. The different multipath components are assumed to be reasonably uncorrelated. When the assumption is valid and a sufficient number of fingers are used, maximum ratio combining of the fingers results in a quite simple receiver technology with good performance.
Channel Estimation Overview
The overall frame structure for the physical channels of the exemplary W-CDMA scheme are depicted in FIG. 2. The transmitted base band signal, si,j,k, is given by
si,j,k=ci,j,kxc2x7uj,kxe2x80x83xe2x80x83(1)
where ci,j,k is the complex spreading sequence and uj,k represents the jth complex symbol in slot k. The notation above gives the signals of interest for chip i in symbol j and slot k, where i=0,1, . . . Sixe2x88x921 and j=0,1, . . . Nsxe2x88x921. The spreading factor is given by Sf and Ns is the number of symbols per slot. For the W-CDMA system, the chip rate is 4.096e6 chip per second (cbps) and                               N          s                =                              2560                          S              f                                .                                    (        2        )            
The long code is cyclically repeated every frame. In order to get a coherent receiver, the channel corruption ĥj,kxe2x88x92nB (of amplitude and phase) for each symbol j in slot kxe2x88x92nB needs to be estimated. Due to the different arrival times of the multipath components, the channel corruptions are correspondingly different for each multipath component. In order to perform Maximum Ratio Combining (MRC) the channel corruption needs to be estimated for each of the multipath components that is synchronized to a RAKE finger 101. The first step in the channel estimation procedure is to obtain a primary channel estimate {overscore (h)}k for each slot. A channel estimate, ĥj,kxe2x88x92B for each symbol j in slot kxe2x88x92nB is then obtained, based on m consecutive primary channel estimates, where mxe2x89xa7nB. The parameter nB is the number of slots that are buffered. The distribution of the channel characteristics in the multipath components is dependent on the environment and can, for example, be Rayleigh distributed. The amplitude and phase variation of consecutive primary channel estimates depend on the one hand on the Rayleigh distribution and on the other hand on the Doppler frequency.
The principle blocks related to one exemplary finger 101 of the RAKE receiver are depicted in FIG. 3. As an overview to its operation, the RAKE finger 101 performs spreading code correlation, integration over a symbol, and estimation of the channel using a priori known pilot symbols. The channel estimate is then used to compensate for the channel distortion. The operation of the RAKE finger 101 will now be described in greater detail.
The received signal in a W-CDMA system is
ri,j,k=si,j,kxc2x7hi,j,k+ni,j,kxe2x80x83xe2x80x83(3)
where ni,j,k is the interference modulated as complex valued Additive White Gaussian Noise (AWGN) with the variance N0. The despread received signal is then                                           r                          j              ,              k                                =                                    1                              S                f                                      ·                                          ∑                                  i                  =                  0                                                                      S                    f                                    -                  1                                            ⁢                              xe2x80x83                            ⁢                                                c                                      i                    ,                    j                    ,                    k                                    *                                ·                                  (                                                                                    c                                                  i                          ,                          j                          ,                          k                                                                    ·                                              u                                                  j                          ,                          k                                                                    ·                                              h                                                  i                          ,                          j                          ,                          k                                                                                      +                                          n                                              i                        ,                        j                        ,                        k                                                                              )                                                                    ⁢                  
                ⁢                              r                          j              ,              k                                =                                                    u                                  j                  ,                  k                                            ·                              h                                  j                  ,                  k                                                      +                                                            n                  ~                                                  j                  ,                  k                                            .                                                          (        4        )            
In each RAKE finger 101 the received signal, which is aligned to corresponding path delay, is despread by multiplying with the conjugated code c*i,j,k. In the exemplary embodiment of FIG. 3, this is performed by the first multiplier 401. A first integration device 403 then performs the succeeding integration over a symbol to yield the received symbols, rj,k, where xc3x1j,k also is considered as white Gaussian noise with variance N0/Sf. The noise is correspondingly suppressed by a factor Sf compared to ni,j,k. For the W-CDMA system, the first Np symbols in each slot are a priori known pilot symbols. These Np symbols are routed, by for example a switch 405, to a second multiplier 407. The second multiplier 407 multiplies the received pilot symbols by the conjugated a priori known pilot symbols, uj,k*. The resultant product of this multiplication is then supplied to a second integration device 409, which generates a primary channel estimate {overscore (h)}k for slot k. Mathematically, this is seen as                                                         h              ~                        k                    =                                    1                              N                p                                      ·                                          ∑                                  j                  =                  0                                                                      N                    p                                    -                  1                                            ⁢                              xe2x80x83                            ⁢                                                u                                      j                    ,                    k                                    *                                ·                                  (                                                                                    u                                                  j                          ,                          k                                                                    ·                                              h                                                  j                          ,                          k                                                                                      +                                                                  n                        ~                                                                    j                        ,                        k                                                                              )                                                                    ⁢                  
                ⁢                                            h              ~                        k                    =                                                    h                _                            k                        +                                          n                ^                            k                                                          (        5        )            
For reasons similar to that described above with respect to the noise in Eq. (4) {circumflex over (n)}k is considered to be white Gaussian noise with a variance given by N0/(Npxc2x7Sf).
Consider a refined channel estimator 411 that uses multiple primary channel estimates to obtain a channel estimate ĥj,kxe2x88x92nB for symbol j in slot kxe2x88x92nB by means of linear combination:
ĥj,kxe2x88x92nB=Gjxc2x7{tilde over (H)}Np less than jxe2x89xa6Ns,xe2x80x83xe2x80x83(6)
where nB is the number of slots to buffer. The vector Gj is the vector of m filter coefficients that are associated with the refined channel estimate for symbol j:
Gj=[gkxe2x88x92m, . . . , gkxe2x88x921, gk].xe2x80x83xe2x80x83(7)
{tilde over (H)} is the vector of the primary channel estimates from m slots
{tilde over (H)}=[{tilde over (h)}kxe2x88x92m, . . . , {tilde over (h)}kxe2x88x921, {tilde over (h)}k]T.xe2x80x83xe2x80x83(8)
The filter coefficients Gj minimize the mean-squared error
E{(hj,kxe2x88x92nBxe2x88x92Gjxc2x7{overscore (H)})*(hj,kxe2x88x92nBxe2x88x92Gjxc2x7{overscore (H)})},xe2x80x83xe2x80x83(9)
where E{ } is the well-known expectation function.
This brings about that the minimum mean-squared error (MMSE) estimator of hj,kxe2x88x92nB satisfies the condition.
E{(hj,kxe2x88x92nBxe2x88x92Gjxc2x7{tilde over (H)})xc2x7{tilde over (H)}H}=0,xe2x80x83xe2x80x83(10)
where {tilde over (H)}H denotes the Hermetian transpose of the matrix {tilde over (H)}(see Louis L. Scharf, Statistical Signal Processing, Detection, Estimation, and Time Series Analysis, Addison Wesley 19038, 1991). The condition could be rewritten as
Rh{overscore (h)}xe2x88x92Gjxc2x7R{tilde over (h)}{tilde over (h)}=0,xe2x80x83xe2x80x83(11)
where Rh{overscore (h)} is the cross-covariance between the channel for symbol j in slot kxe2x88x92nB and the m primary channel estimates, and R{tilde over (H{tilde over (H)})} is the cross co-variance between all the m primary channel estimates. The filter coefficients Gj are given by
Gj=Rh{tilde over (h)}xc2x7R{tilde over (h)}{tilde over (h)}xe2x88x921,xe2x80x83xe2x80x83(12)
To assist with further explanations, a positioning function p(j,k) is defined as
p(j,k)=Tsxc2x7(jxc2x7Sf+kxc2x7Ns)j=0, 1, . . . Nsxe2x80x83xe2x80x83(13)
where Ts is the duration of a symbol j in slot k. Also, the time-correlation, xcfx81(xcex94t), in the channel determines how fast the channel fluctuates. If one assumes that the power spectrum density of channel hj,k is given by Jakes model (see W. C. Jakes, Microwave Mobile Communications, IEEE Press, 1974), then
xcfx81(xcex94t)=J0(2xcfx80fdxcex94t),xe2x80x83xe2x80x83(14)
where J0(2xcfx80fdxcex94t) is a Bessel function of the first kind and of order zero, and where fd is the Doppler frequency. By using the positioning function in the correlation function,
Rh{overscore (h)}=|{tilde over (h)}|2xc2x7[xcfx81(p(j,kxe2x88x92nB)xe2x88x92p(1,kxe2x88x92m)), . . . , xcfx81(p(j,kxe2x88x92nB)xe2x88x92p(1,k))].xe2x80x83xe2x80x83(15)
Furthermore, R{tilde over (H{tilde over (H)})} is given by                                           R                                          h                ~                            ⁢                              h                ~                                              =                                                    "LeftBracketingBar"                                  h                  _                                "RightBracketingBar"                            2                        ·                          [                              xe2x80x83                            ⁢                                                                                                                  ρ                        ⁡                                                  (                          0                          )                                                                    +                                                                        N                          0                                                                                                                                                                    "LeftBracketingBar"                                                                  h                                  _                                                                "RightBracketingBar"                                                            2                                                        ·                                                          S                              f                                                                                ⁢                                                      N                            p                                                                                                                                                    …                                                                              ρ                      ⁢                                              xe2x80x83                                            ⁢                                              (                                                                              p                            ⁡                                                          (                                                              1                                ,                                                                  k                                  -                                  m                                                                                            )                                                                                -                                                      p                            ⁡                                                          (                                                              1                                ,                                k                                                            )                                                                                                      )                                                                                                                                  …                                                        …                                                        …                                                                                                              ρ                      ⁢                                              xe2x80x83                                            ⁢                                              (                                                                              p                            ⁡                                                          (                                                              1                                ,                                k                                                            )                                                                                -                                                      p                            ⁡                                                          (                                                              1                                ,                                                                  k                                  -                                  m                                                                                            )                                                                                                      )                                                                                                  …                                                                                                      ρ                        ⁡                                                  (                          0                          )                                                                    +                                                                        N                          0                                                                                                                                                                    "LeftBracketingBar"                                                                  h                                  _                                                                "RightBracketingBar"                                                            2                                                        ·                                                          S                              f                                                                                ⁢                                                      N                            p                                                                                                                                                          ⁢                              xe2x80x83                            ]                                      ,                            (        16        )            
where |{overscore (h)}|2 is the average power of the channel and N0 the average variance of the interference. The average Signal to Interference Ratio (SIR) per symbol is then defined as                     SIR        =                                            "LeftBracketingBar"                              h                _                            "RightBracketingBar"                        2                                              S              f                        ·                          N              0                                                          (        17        )            
It can be seen, then, that in order for the RAKE finger 101 to function, it is necessary for the refined channel estimator 411 to determine the filter coefficients, Gj. However, the straightforward approach, in which the filter coefficients are calculated directly in accordance with Eq. (12), imposes a heavy computational load on the receiver. This is primarily due to the need to perform a matrix inversion as indicated in Eq. (12), coupled with the fact that the filter coefficients Gj used in Eq. (6) need to be updated for each slot. Thus, there is a need for techniques and apparatuses that can determine channel estimates in a computationally less intensive manner.
It is therefore an object of the present invention to provide techniques and apparatuses capable of determining channel estimates without the burdensome computational load imposed by conventional techniques.
In accordance with one aspect of the invention, the foregoing and other objects are achieved in methods and apparatuses for determining a communications channel estimate in a receiver, in which a polynomial expression is used to determine a set of approximated filter coefficients. The approximated filter coefficients are then used to determine the communications channel estimate.
In another aspect of the invention, polynomial coefficients for the polynomial expression are determined by supplying an address to a polynomial coefficient table having stored therein at least one set of polynomial coefficients. The polynomial coefficients supplied at an output of the polynomial coefficient table are then used as the polynomial coefficients for the polynomial expression.
The address may be derived at least in part from a Doppler frequency value of a received signal. In some embodiments, this may include quantizing the Doppler frequency value; and using the quantized Doppler frequency value as the address.
In still another aspect of the invention, polynomial coefficients for the polynomial expression may be determined by using a second polynomial expression to determine a set of approximated polynomial coefficients. The approximated polynomial coefficients are then used as part of the polynomial expression that is used to determine the set of approximated filter coefficients.
In yet another aspect of the invention, the polynomial expression that is used to determine the set of approximated filter coefficients is a function of a signal to interference ratio of a received signal, and of a Doppler frequency of the received signal.